Teaching Mathematics using an approach that is both conceptual and procedural - ​

Keys 7 - 9 unpacked

Keys #7-9 focus on the paradigm shift required to transition from a procedural approach and outlines a path forward.​

Key #7

As has already been suggested, adopting the hybrid conceptual approach requires a very different pedagogy to a traditional procedural approach. Although the hybrid conceptual approach is easy to administer once sufficient experience has been gained, the transition from a traditional procedural approach to the hybrid conceptual approach requires time and guidance.

Key #8

The transition requires a paradigm shift in the teachers’ thinking and classroom management. Ideally, teachers making the shift will receive some quality, ongoing professional guidance which requires them to implement a range of well-structured, student-centred, conceptually-based activities.

Key #9

Learn Implement Share provides long-term guidance to mathematics teachers regarding the transition via two comprehensive online courses. Each course caters for individuals as well as department-wide TEAMs. (Links to information are provided below.)

Keys 7-9 unpacked

We all know what the traditional procedural approach looks like. Most of us were taught this way and many of us base our teaching, to a large degree, on it today. The difference between an ‘average’ procedural approach and what we could call a quality, explicit procedural approach lies in the level of classroom management, teacher instruction, quality questioning, lesson structure, lesson summaries and so on. Regardless, if ten teachers were to describe a procedural approach we would recognise each as a description of the same approach.

However, if ten teachers were to describe a conceptual approach we would likely end up with descriptions of multiple, different approaches.

By describing the Learn Implement Share hybrid conceptual approach as highly-structured, student-centred, conceptually-based and incorporating the explicit teaching of procedures we help to separate it from the common procedural approach and also from other (perhaps) less-structured conceptual approaches that place less emphasis on the explicit teaching of procedures.

Clearly, the two approaches - procedural and hybrid-conceptual are very, very different.

The mistake often made by presenters

Presenters often make the mistake - and I’ll put my hand up at this point for past failings - of promoting conceptually-based activities to teachers without mentioning the need for a very different pedagogy to successfully run conceptually-based activities.

The assumption from such presentations is that teachers new to a conceptually-based approach will be able to run the activities with their students ‘the next day’. This is despite the fact that the critical information - that conceptually-based activities will fail if delivered using the common teacher-directed approach - has neither been mentioned nor expanded upon.

What often follows is teachers attempting to implement the conceptual activities via their familiar teacher-directed pedagogy, finding nothing impressive in them (because the activities did not work well) and then retreating to the comfort of what they know - traditional proceduralism.

The reality is we cannot expect a teacher who is only comfortable with a teacher-directed procedural approach to make the transition unless they have gained classroom-based guidance with the required pedagogy.

Ideally, what is required is a substantial program which is collaborative, self-reflective, builds a foundation for the transition, presents numerous examples of conceptually-based strategies and activities and through which teachers implement the strategies and reflect and report on their implementation experiences.